A density functional theory study of electric potential saturation: planar geometry

TL;DR

This study uses density functional theory to analyze electric potential saturation near a charged plane in an electrolyte, identifying conditions where the potential becomes independent of the plane's charge at high charge densities.

Contribution

It provides a general theoretical condition for electrostatic potential saturation in planar geometries with arbitrary micro-ion distributions.

Findings

Derived a necessary and sufficient condition for potential saturation.

Showed potential saturation occurs when the electrostatic potential becomes independent of the bare charge.

Applicable to systems with complex micro-ion profiles in electrolytes.

Abstract

We investigate the possibility of electrostatic potential saturation, which may lead to the phenomenon of effective charge saturation. The system under study is a uniformly charged infinite plane immersed in an arbitrary electrolyte made up of several micro-species. To describe the electric double layer, we use a generic density functional theory in which the local micro-ionic density profiles are arbitrary functions of the local electrostatic potential. A necessary and sufficient condition is obtained for saturation, whereby the electrostatic potential created by the plane becomes independent of its bare charge, provided the latter is large enough.